The Theory of Scintillation with Applications in Remote Sensing

Charles Rino

• Publisher: Wiley-IEEE Press
• Year: 2011
• Print ISBN: 9780470644775
• eBook ISBN: 9781118011744
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

In order to truly understand data signals transmitted by satellite, onemust understand scintillation theory in addition to well established theories of EM wave propagation and scattering. Scintillation is a nuisance in satellite EM communications, but it has stimulated numerous theoretical developments with science applications. This book not only presents a thorough theoretical explanation of scintillation, but it also offers a complete library of MATLAB codes that will reproduce the book examples. The library includesGPS coordinate manipulations, satellite orbit prediction, and earth mean magnetic field computations.

The subect matter is for EM researchers; however, also theory is relevant to geophysics, acoustics, optics and astoronomy.

CHAPTER 1

INTRODUCTION

Twinkle, twinkle, little star. How I wonder what you are.

—Jayne Taylor

Scintillation observations have been used to identify and diagnose irregular structure in highly varied propagation media. Scintillation research has led to contributions in atmospheric physics, ionospheric physics, geophysics, ocean acoustics, and astronomy. The collection of papers published in the book Wave Propagation in Random Media (Scintillation) [7] provides a sampling of these diverse applications of scintillation phenomenology. Scintillation can be defined formally as a random modulation imparted to propagating wave fields by structure in the propagation medium. A familiar example is the twinkling of stars in the night sky, which is caused by turbulence in the earth’s atmosphere. Structure in a propagation medium manifests itself as changes in the refractive index. From the ray theory of propagation it is known that local refractive-index enhancements can focus bundles of rays that pass through them. The wave field intensity variations identified as scintillation can be explained by this ray-focusing mechanism. Thus, scintillation phenomena are well understood and widely exploited, but nonethe-less it is difficult to find a definitive treatment of the theory of scintillation. Introductory propagation theory addresses the space time evolution of wave fields launched in homogeneous media. Scattering theory addresses secondary (scattered) wave fields that are initiated wherever propagating wave fields encounter abrupt changes (steep gradients) in the material properties of the propagation medium. Scintillation theory lies somewhere in between the conventional theories of propagation and scattering.

This book has two objectives. The first objective is to develop a theory of scintillation that characterizes propagation media that support scintillation and the propagation phenomena that ensue. The second objective is to exploit numerical simulations as a research analysis tool. Modern and widely available computational resources support the application of high-fidelity and high-resolution simulations. The insights gained through simulations would be very difficult to obtain from analytic results and experimental observations alone.

The theoretical development presented in Chapters 2, 3, and 4 proceeds from an electromagnetic (EM) engineering framework with examples specific to propagation in the Earth’s atmosphere and ionosphere. However, the formalism can be adapted to acoustic wave propagation in water or solid matter. This introductory chapter summarizes established results from EM theory that are used extensively in the development of scintillation theory and its applications. The interpretation of scintillation as a modulation imparted to a wave field that would otherwise be characterized completely by conventional propagation theory is emphasized as a link to real-world measurements and as an entree to modern digital signal processing techniques.

Chapter 2 presents a rigorous development of scintillation theory as a natural extension of propagation in strictly homogeneous media. Propagation media that admit structure with spatial variations that do not change over wavelength-scale distances are referred to as weakly inhomogeneous media. The implicit small-gradient constraint supports a modified wave equation that incorporates the structure as a multiplicative interaction with the total wave field. The wave equation thus modified is the starting point for all theoretical developments that address propagation in weakly inhomogeneous media. However, scintillation theory requires an additional assumption that sets it apart from other propagation phenomena. To make this requirement explicit, the modified wave equation is rewritten as an equivalent pair of coupled first-order differential equations that individually characterize propagation in opposite directions designated as forward and backward. Scintillation theory is based on the forward approximation, which neglects backward propagating waves induced by the interaction of the wave field with the weakly inhomogeneous structure. The resulting forward propagation equation (FPE) provides the mathematical connection between wave field observables and the structure that induces the modulation defined as scintillation. In mathematical terms, the theory of scintillation is a characterization of the domain and range of the FPE. The more familiar parabolic wave equation follows from the parabolic approximation to the propagation operator in the FPE.

Chapter 2 concludes with simulation examples that illustrate the broad range of propagation phenomena supported by the FPE, including beam propagation and propagation in highly refracting backgrounds. Beam propagation is introduced to demonstrate the evolution of a propagating wave field as launched by real devices. The beam wave field is formally a carrier onto which scintillation structure is imparted. The final example demonstrates weak and strong scintillation in power-law environments via simulations. Plane-wave excitation is introduced as a way to avoid the need to model source and background details. In effect, plane-wave results characterize the propagation-induced modulation directly, although an adjustment must be made to accommodate wavefront curvature. The wavefront curvature correction is described in Chapter 4, where the corrections are used explicitly.

Chapter 3 develops the statistical theory of scintillation, which is a special case of the broader theory of scintillation supported by the FPE. The statistical theory provides a formalism for calculating statistical measures of the complex field in terms of statistical measures of the in situ structure. The complex field measures include probability distributions, spatial, temporal, and frequency coherence functions, spectral density functions, and structure functions. The main development in Chapter 3 is the derivation of a set of differential equations that individually characterize the complex-field moments of all orders in terms of summations of phase structure functions. The moment equations are themselves first-order differential equations with a structure similar to the underlying FPE equation. Key results that strike a balance between complexity and practical utility are presented, but an attempt has been made to reference ...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright
• Dedication
• Preface
• Chapter 1: Introduction
• Chapter 2: The Forward Propagation Equation
• Chapter 3: The Statistical Theory of Scintillation
• Chapter 4: Beacon Satellite Scintillation
• Chapter 5: System Applications of Scintillation Theory
• Chapter 6: Scattering and Boundaries
• Appendix A
• References
• Index